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Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder.…
In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-order optimization, stochastic approximation with…
The main purpose of this paper is to study the Dynamical behaviors of a stochastic SIS epidemic model using mean-reverting inhomogeneous geometric brownian motion process. First we demonstrate the existence of a global-in-time solution and…
The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In…
We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the…
While noise is generally associated with uncertainties and often has a negative connotation in engineering, living organisms have evolved to adapt to (and even exploit) such uncertainty to ensure the survival of a species or implement…
In the present paper we provide the closed form of the path-like solutions for the logistic and $\theta$-logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their…
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive…
This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has…
In the present article, we construct a logarithm transformation based Milstein-type method for the stochastic susceptible-infected-susceptible (SIS) epidemic model evolving in the domain (0,N). The new scheme is explicit and unconditionally…
An enviromental-random effect over a deterministic population mo\-del, a resource ({\it e.g.}, a fish stock) is introduced. It is assumed that the harvest activity is concentrated at a non predetermined sequence of instants, at which the…
In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical…
Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…